Speed of Light

Concept Of Physics

H C Verma

1   1. In an experiment to measure the speed of light by Fizeau's apparatus, following data are used : Distance between the mirrors = 12.0 km, Number of teeth in the wheel = 180. Find the minimum angular speed of the wheel for which the image is not seen.

Solution :

In the given Fizeau apparatus, $\\$ D=12km=12$\times10^3$km $\\$ n=180 $\\$ c=3$\times10^8m/s.$ $\\$ We know, c=$\frac{2Dn\omega}{\pi} $ $\\$ $\Rightarrow \omega=\frac{\pi c}{2Dn} rad/sec=\frac{\pi c}{2Dn}\times\frac{180}{\pi} deg/sec $ $\\$ $ \Rightarrow \omega = \frac{180\times3\times10^8}{24\times10^3\times180}=1.25\times10^4 deg/sec$ $\\$

2   2. In an experiment with Foucault's apparatus, the various distances used are as follows : Distance between the rotating and the fixed mirror = 16 m Distance between the lens and the rotating mirror = 6 m,

Solution :

In the given Focault expirement $\\$, R=Distance between fixed and rotating mirror=16m $\\$ $\omega=Angular speed= 356rev/'=356\times2rad/sec $ $\\$ b=distance between lens and rotating mirror = 6m $\\$ a= distance between source and lens=2m $\\$ s=shift in image = 0.7cm= $0.7\times10^-3 m$ $\\$ So, speed of light is given by, $\\$ C=$ \frac{4R^2\omega a}{s(R+b)}=\frac{4\times16^2\times356\times2 \pi \times 2}{0.7\times 10^{-3}(16+6)}=2.975\times 10^8 m/s $ $\\$

3   3. In a Michelson experiment for measuring speed of light, the distance traveled by light between two reflections from the rotating mirror is 4.8 km. The rotating mirror has a shape of a regular octagon. At what minimum angular speed of the mirror (other than zero) the image is formed at the position where a non-rotating mirror forms it ?

Solution :

In the given Michelson experiment, $\\$ D=4.8km=4.8$\times10^3m $ $\\$ N=8 $\\$ We know, c=${D\omega N}{2\pi}$ $\\$ $\Rightarrow \omega= \frac{2\pi c}{DN}rad/sec=\frac{c}{DN} rev/sec=\frac{3\times10^8}{4.8\times10^3\times8}=7.8\times10^3 rev/sec $ $\\$